Another way of looking at this:
Never do -- or avoid -- anything
without a good
reason. Whether it's parallel fifths or parallel
thirds or sixths or tenths or even parallel flat
Or parallel motion itself.
Parellel motion emphasizes the importance of a
given line (regardless of the parallel interval).
And the parallel interval decides both the
strength and the color of that emphasis. A very
(harmonically) strong interval like a fifth lends
greater prominence, while coloring the line with
a hollow, tonally ambiguous nature. A major third
or tenth imparts lesser emphasis, while sweetening
the line with implications of the major scale.
Dissonant intervals, a flat ninth, say, will
actually weaken a line with harmonic ambiguity,
but bring emphasis by the bitterness added to it.
All of this, however, is stylistically contextual;
in that the ear establishes harmonic relevance of
given intervals within the framework of the idiom.
In strict Classical style, parallel fifths will
generally stand forth in a texture due to the
great importance of the interval in that harmonic
framework. In a tightly constrained pentatonic
piece -- they'd often just sound... odd, misplaced.
But in many modern styles with richer methodologies
of achieving tonal relationships, they'd likely go